Equally likely outcomes
When every possible outcome of an experiment has the same chance of happening, we say the outcomes are equally likely. A fair coin, a fair die and a spinner with equal sectors all give equally likely outcomes. The set of all possible outcomes is called the sample space.
Key idea
P(event) = (number of favourable outcomes) ÷ (total number of outcomes in the sample space). This is the theoretical probability.
Using the formula
First list or count the outcomes in the sample space. Then count how many of them are favourable to the event. Divide the two numbers and simplify the fraction. The answer always lies between 0 (impossible) and 1 (certain).
Worked example
A fair die is rolled once. Find the probability of getting a number greater than 4.
Sample space = {1, 2, 3, 4, 5, 6}, so total outcomes = 6.
Favourable outcomes (greater than 4) = {5, 6}, so there are 2.
P(number > 4) = 2 ÷ 6 = 1 ÷ 3.
Another example
A bag contains 3 red, 2 blue and 5 green marbles, all the same size. The total is 3 + 2 + 5 = 10 marbles. Picking any marble is equally likely. P(blue) = 2 ÷ 10 = 1 ÷ 5.
Remember
- Outcomes must be equally likely for this formula to work.
- Always simplify the fraction if possible.
- Probability 0 means impossible; probability 1 means certain.